Ridge Regression
Change: Model is run multiple times with different train and test sets
library(tidyverse)
library(knitr)
library(plotly) ; library(viridis) ; library(gridExtra) ; library(RColorBrewer)
library(biomaRt)
library(Rtsne)
library(caret) ; library(ROCR) ; library(car)
library(corrplot)
library(expss) ; library(knitr)
SFARI_colour_hue = function(r) {
pal = c('#FF7631','#FFB100','#E8E328','#8CC83F','#62CCA6','#59B9C9','#b3b3b3','#808080','gray','#d9d9d9')[r]
}Background
In 20_04_07_LR.html we performed a logistic regression but we discovered that the features were strongly correlated. This inflates the standard error of the coefficients, making them no longer interpretable.
# Clusterings
clustering_selected = 'DynamicHybridMergedSmall'
clusterings = read_csv('./../Data/clusters.csv')
clusterings$Module = clusterings[,clustering_selected] %>% data.frame %>% unlist %>% unname
assigned_module = data.frame('ID' = clusterings$ID, 'Module' = clusterings$Module)
# Original dataset
original_dataset = read.csv(paste0('./../Data/dataset_', clustering_selected, '.csv'), row.names=1)
# Model dataset
load('./../Data/LR_model.RData')
# Add gene symbol
getinfo = c('ensembl_gene_id','external_gene_id')
mart = useMart(biomart='ENSEMBL_MART_ENSEMBL', dataset='hsapiens_gene_ensembl',
host='feb2014.archive.ensembl.org')
gene_names = getBM(attributes=getinfo, filters=c('ensembl_gene_id'), values=rownames(dataset), mart=mart)Variance Inflation Factor (VIF) and correlation plot
# VIF
plot_data = data.frame('Feature' = car::vif(fit) %>% sort %>% names,
'VIF' = car::vif(fit) %>% sort %>% unname) %>%
mutate(outlier = VIF>10)
plot_data %>% ggplot(aes(reorder(Feature, -VIF), VIF, fill = !outlier)) + geom_bar(stat='identity') + scale_y_log10() +
geom_hline(yintercept = 10, color = 'gray', linetype = 'dashed') + xlab('Model Features') + theme_minimal() +
theme(legend.position = 'none', axis.text.x = element_text(angle = 90, hjust = 1))
# Correlation plot
corrplot.mixed(cor(train_set[,-ncol(train_set)]), lower = 'number', lower.col = 'gray', number.cex = .6, tl.pos = 'l', tl.col = '#666666')
rm(getinfo, mart, clusterings)Possible solutions to Multicollinearity:
Remove all variables with a VIF>10: We would lose all but three of our variables, not ideal
Do Principal Component Regression: We would lose the relation between the prediction and the original features, which would be interesting to study
Don’t do anything: Multicollinearity affects the coefficients and p-values of the regression, but it doesn’t affect the predictions, precision of the predictions or the goodness-of-fit statistics ref, but as with the previous option, we cannot study the coefficients of the regression
Use Ridge Regression
Ridge Regression
Notes:
Running the model multiple times to get more acurate measurements of its performance
Over-sampling positive samples in the training set to obtain a 1:1 class ratio
### DEFINE FUNCTIONS
# Create positive training set including all SFARI scores
positive_sample_balancing_SFARI_scores = function(p, seed){
set.seed(seed)
positive_train_idx = c()
for(score in 1:6){
score_genes = rownames(original_dataset)[rownames(original_dataset) %in% rownames(dataset) & original_dataset$gene.score == score]
score_idx = which(rownames(dataset) %in% score_genes)
score_train_idx = sample(score_idx, size = ceiling(p*length(score_idx)))
positive_train_idx = c(positive_train_idx, score_train_idx)
}
return(positive_train_idx)
}
create_train_test_sets = function(p, over_sampling_fold, seed){
### CREATE POSITIVE TRAINING SET (balancing SFARI scores and over-sampling)
positive_train_idx = positive_sample_balancing_SFARI_scores(p, seed)
add_obs = sample(positive_train_idx, size = ceiling(over_sampling_fold*length(positive_train_idx)), replace=TRUE)
positive_train_idx = c(positive_train_idx, add_obs)
### CREATE NEGATIVE TRAINING SET
negative_idx = which(!dataset$SFARI)
negative_train_idx = sample(negative_idx, size = length(positive_train_idx))
### CREATE TRAIN AND TEST SET
train_set = dataset[sort(c(positive_train_idx, negative_train_idx)),]
test_set = dataset[-unique(c(positive_train_idx, negative_train_idx)),]
return(list('train_set' = train_set, 'test_set' = test_set))
}
run_model = function(p, over_sampling_fold, seed){
# Create train and test sets
train_test_sets = create_train_test_sets(p, over_sampling_fold, seed)
train_set = train_test_sets[['train_set']]
test_set = train_test_sets[['test_set']]
# Train Model
train_set$SFARI = train_set$SFARI %>% as.factor
lambda_seq = 10^seq(1, -4, by = -.1)
set.seed(123)
fit = train(SFARI ~., data = train_set, method = 'glmnet', trControl = trainControl('cv', number = 10),
tuneGrid = expand.grid(alpha = 0, lambda = lambda_seq))
# Predict labels in test set
predictions = fit %>% predict(test_set, type='prob')
preds = data.frame('ID'=rownames(test_set), 'prob'=predictions$`TRUE`) %>% mutate(pred = prob>0.5)
# Measure performance of the model
acc = mean(test_set$SFARI==preds$pred)
pred_ROCR = prediction(preds$prob, test_set$SFARI)
AUC = performance(pred_ROCR, measure='auc')@y.values[[1]]
# Extract coefficients from features
coefs = coef(fit$finalModel, fit$bestTune$lambda) %>% as.vector
return(list('acc' = acc, 'AUC' = AUC, 'preds' = preds, 'coefs' = coefs))
}
### RUN MODEL
# Parameters
p = 0.8
over_sampling_fold = 3
n_iter = 100
seeds = 123:(123+n_iter-1)
# Store outputs
acc = c()
AUC = c()
predictions = data.frame('ID' = rownames(dataset), 'SFARI' = dataset$SFARI, 'prob' = 0, 'pred' = 0, 'n' = 0)
coefs = data.frame('var' = c('Intercept', colnames(dataset[,-ncol(dataset)])), 'coef' = 0)
for(seed in seeds){
# Run model
model_output = run_model(p, over_sampling_fold, seed)
# Update outputs
acc = c(acc, model_output[['acc']])
AUC = c(AUC, model_output[['AUC']])
preds = model_output[['preds']]
coefs$coef = coefs$coef + model_output[['coefs']]
update_preds = preds %>% dplyr::select(-ID) %>% mutate(n=1)
predictions[predictions$ID %in% preds$ID, c('prob','pred','n')] = predictions[predictions$ID %in% preds$ID, c('prob','pred','n')] + update_preds
}
coefs = coefs %>% mutate(coef = coef/n_iter)
predictions = predictions %>% mutate(prob = prob/n, pred_count = pred, pred = prob>0.5)
rm(p, over_sampling_fold, seeds, update_preds, positive_sample_balancing_SFARI_scores, create_train_test_sets, run_model)To summarise in a single value the predictions of the models:
prob = Average of all the probabilities
pred = 1 if prob>0.5, 0 otherwise
test_set = predictions %>% filter(n>0) %>% left_join(dataset %>% mutate(ID = rownames(.)) %>% dplyr::select(ID, GS, MTcor), by = 'ID')
rownames(test_set) = predictions$ID[predictions$n>0]Performance metrics
Confusion matrix
conf_mat = test_set %>% apply_labels(SFARI = 'Actual Labels',
prob = 'Assigned Probability',
pred = 'Label Prediction')
cro(conf_mat$SFARI, list(conf_mat$pred, total()))|  Label Prediction |  #Total | |||
|---|---|---|---|---|
| Â FALSEÂ | Â TRUEÂ | Â | ||
|  Actual Labels | ||||
| Â Â Â FALSEÂ | 9730 | 5407 | Â | 15137 |
| Â Â Â TRUEÂ | 358 | 539 | Â | 897 |
|    #Total cases | 10088 | 5946 |  | 16034 |
rm(conf_mat)Accuracy
cat(paste0('ACCURACY: mean = ', round(mean(acc),4), ' SD = ', round(sd(acc),4)))## ACCURACY: mean = 0.6396 SD = 0.0069ROC Curve
cat(paste0('AUC: mean = ', mean(AUC), ' SD = ', sd(AUC)))## AUC: mean = 0.670549396655147 SD = 0.0192981599597913pred_ROCR = prediction(test_set$prob, test_set$SFARI)
roc_ROCR = performance(pred_ROCR, measure='tpr', x.measure='fpr')
auc = performance(pred_ROCR, measure='auc')@y.values[[1]]
plot(roc_ROCR, main=paste0('ROC curve (AUC=',round(auc,2),')'), col='#009999')
abline(a=0, b=1, col='#666666')
Lift Curve
lift_ROCR = performance(pred_ROCR, measure='lift', x.measure='rpp')
plot(lift_ROCR, main='Lift curve', col='#86b300')
rm(pred_ROCR, roc_ROCR, AUC, lift_ROCR)Coefficients
MTcor has a very small coefficient and Gene Significance has a negative coefficient (!)
gene_corr_info = dataset %>% mutate('ID' = rownames(dataset)) %>% dplyr::select(ID, MTcor, SFARI) %>% left_join(assigned_module, by ='ID') %>%
mutate(Module = gsub('#','',Module))
coef_info = coefs %>% mutate('feature' = gsub('MM.','',var)) %>% left_join(gene_corr_info, by = c('feature' = 'Module')) %>%
dplyr::select(feature, coef, MTcor, SFARI) %>% group_by(feature, coef, MTcor) %>% summarise('SFARI_perc' = mean(SFARI)) %>%
arrange(desc(coef))
kable(coef_info %>% dplyr::select(feature, coef) %>% rename('Feature' = feature, 'Coefficient' = coef),
align = 'cc', caption = 'Regression Coefficients')| Feature | Coefficient |
|---|---|
| FF62BC | 1.0193924 |
| 00A7FF | 0.6409614 |
| FE6E8A | 0.5537652 |
| 00BF7D | 0.5186754 |
| 00BA38 | 0.5089766 |
| 00BFC4 | 0.4421878 |
| D376FF | 0.3966287 |
| 00BCD8 | 0.3877020 |
| 00C0AF | 0.3398744 |
| D89000 | 0.2897373 |
| 00C097 | 0.1894138 |
| 39B600 | 0.1828604 |
| F8766D | 0.1794108 |
| EF7F49 | 0.1381873 |
| 6BB100 | 0.0798353 |
| F564E3 | 0.0697580 |
| E58700 | 0.0664270 |
| absGS | 0.0349896 |
| B79F00 | 0.0225067 |
| FF67A4 | 0.0067750 |
| MTcor | -0.0031499 |
| 00B0F6 | -0.0149717 |
| A3A500 | -0.0681002 |
| GS | -0.1314690 |
| E76BF3 | -0.1357313 |
| B983FF | -0.1912169 |
| Intercept | -0.2056533 |
| FD61D1 | -0.2101999 |
| 00BD5F | -0.2324720 |
| 8AAB00 | -0.2491964 |
| C99800 | -0.2767617 |
| 9590FF | -0.4379413 |
| 00B7E9 | -0.5280243 |
| 619CFF | -0.6140371 |
- There is a positive relation between the coefficient assigned to the membership of each module and the percentage of SFARI genes that are assigned to that module
ggplotly(coef_info %>% dplyr::rename('Module' = feature) %>% filter(!is.na(MTcor)) %>%
ggplot(aes(coef, SFARI_perc)) + geom_smooth(method = 'lm', color = 'gray', alpha = 0.1) +
geom_point(aes(id = Module), color = paste0('#',coef_info$feature[!is.na(coef_info$MTcor)])) +
theme_minimal() + xlab('Coefficient') +
ylab('% of SFARI genes in Module'))- There doesn’t seem to be a relation between the coefficient and the correlation of the module and the diagnosis.
This is not a surprise since we knew that there was a negative relation between SFARI genes and Module-Diagnosis correlation from Preprocessing/Gandal/AllRegions/RMarkdowns/20_04_03_WGCNA_modules_EA.html. The fact that there is no relation between coefficient and Module-Diagnosis correlation could even be a good sign that the model is picking some biological signal as well as the SFARI patterns (since the relation with the biological signals is positive)
ggplotly(coef_info %>% dplyr::rename('Module' = feature) %>% filter(!is.na(MTcor)) %>%
ggplot(aes(coef, MTcor)) + geom_smooth(method = 'lm', color = 'gray', alpha = 0.1) +
geom_point(aes(id = Module), color = paste0('#',coef_info$feature[!is.na(coef_info$MTcor)])) +
theme_minimal() + xlab('Coefficient') +
ylab('Module-Diagnosis correlation'))Analyse model
SFARI genes have a slightly higher score distribution than the rest
plot_data = test_set %>% dplyr::select(prob, SFARI)
ggplotly(plot_data %>% ggplot(aes(prob, fill=SFARI, color=SFARI)) + geom_density(alpha=0.3) + xlab('Score') +
geom_vline(xintercept = mean(plot_data$prob[plot_data$SFARI]), color = '#00C0C2', linetype = 'dashed') +
geom_vline(xintercept = mean(plot_data$prob[!plot_data$SFARI]), color = '#FF7371', linetype = 'dashed') +
theme_minimal() + ggtitle('Model score distribution by SFARI Label'))- There seems to be a msall but consistent positive relation between the SFARI scores and the probability assigned by the model
plot_data = test_set %>% mutate(ID=rownames(test_set)) %>% dplyr::select(ID, prob) %>%
left_join(original_dataset %>% mutate(ID=rownames(original_dataset)), by='ID') %>%
dplyr::select(ID, prob, gene.score) %>% apply_labels(gene.score='SFARI Gene score')
cro(plot_data$gene.score)|  #Total | |
|---|---|
|  SFARI Gene score | |
| Â Â Â 1Â | 25 |
| Â Â Â 2Â | 64 |
| Â Â Â 3Â | 191 |
| Â Â Â 4Â | 432 |
| Â Â Â 5Â | 163 |
| Â Â Â 6Â | 22 |
|    None | 15137 |
|    #Total cases | 16034 |
mean_vals = plot_data %>% group_by(gene.score) %>% summarise(mean_prob = mean(prob))
ggplotly(plot_data %>% ggplot(aes(gene.score, prob, fill=gene.score)) + geom_boxplot() +
scale_fill_manual(values=SFARI_colour_hue(r=c(1:6,8,7))) +
ggtitle('Distribution of probabilities by SFARI score') +
xlab('SFARI score') + ylab('Probability') + theme_minimal())rm(mean_vals)Genes with highest scores in test set
Considering the class imbalance in the test set (1:69), there are many more SFARI scores in here (1:3)
3 of the 5 SFARI genes with a score of 1 in the test set are in this top 50 list
There aren’t any SFARI genes with a score of 6
test_set %>% dplyr::select(prob, SFARI) %>% mutate(ID = rownames(test_set)) %>%
arrange(desc(prob)) %>% top_n(50, wt=prob) %>%
left_join(original_dataset %>% mutate(ID=rownames(original_dataset)), by='ID') %>%
left_join(gene_names, by = c('ID'='ensembl_gene_id')) %>%
dplyr::rename('GeneSymbol' = external_gene_id, 'Probability' = prob, 'ModuleDiagnosis_corr' = MTcor, 'GeneSignificance' = GS) %>%
mutate(ModuleDiagnosis_corr = round(ModuleDiagnosis_corr,4), Probability = round(Probability,4),
GeneSignificance = round(GeneSignificance,4)) %>%
dplyr::select(GeneSymbol, GeneSignificance, ModuleDiagnosis_corr, Module, Probability, gene.score) %>%
kable(caption = 'Genes with highest model probabilities from the test set')| GeneSymbol | GeneSignificance | ModuleDiagnosis_corr | Module | Probability | gene.score |
|---|---|---|---|---|---|
| RPRD2 | -0.0922 | -0.6031 | #00BA38 | 0.8433 | None |
| PRDM2 | -0.2518 | 0.0586 | #FE6E8A | 0.8393 | None |
| TANC2 | -0.2348 | -0.6031 | #00BA38 | 0.8367 | 3 |
| EP300 | -0.0234 | 0.1127 | #FF62BC | 0.8346 | 4 |
| MYCBP2 | -0.3975 | -0.6031 | #00BA38 | 0.8316 | None |
| ARID1B | 0.2711 | 0.1127 | #FF62BC | 0.8281 | 1 |
| ANK2 | -0.4368 | -0.9514 | #00C0AF | 0.8258 | 1 |
| SRCAP | -0.3623 | -0.6031 | #00BA38 | 0.8250 | 2 |
| RFX7 | 0.1372 | 0.0586 | #FE6E8A | 0.8243 | None |
| NFAT5 | 0.1035 | 0.0586 | #FE6E8A | 0.8232 | None |
| KMT2A | 0.1347 | 0.7916 | #00C097 | 0.8203 | 1 |
| FMNL1 | -0.2223 | -0.6031 | #00BA38 | 0.8181 | None |
| HUNK | -0.3273 | -0.6750 | #D376FF | 0.8175 | None |
| MBD5 | 0.1943 | 0.0586 | #FE6E8A | 0.8173 | 3 |
| RNF111 | -0.2410 | 0.0586 | #FE6E8A | 0.8170 | None |
| TLE3 | 0.4884 | 0.1127 | #FF62BC | 0.8166 | None |
| SRRM4 | -0.4400 | -0.6031 | #00BA38 | 0.8159 | 5 |
| RAPH1 | -0.0534 | -0.6031 | #00BA38 | 0.8138 | None |
| KMT2D | -0.3255 | -0.6031 | #00BA38 | 0.8127 | None |
| C20orf112 | 0.0314 | 0.1127 | #FF62BC | 0.8089 | None |
| ANK3 | -0.4814 | 0.0586 | #FE6E8A | 0.8078 | 3 |
| HECTD4 | -0.3170 | -0.6031 | #00BA38 | 0.8076 | 3 |
| EP400 | -0.1671 | -0.6031 | #00BA38 | 0.8054 | 3 |
| CREBBP | 0.1431 | 0.1127 | #FF62BC | 0.8050 | 5 |
| KCNJ6 | -0.1379 | -0.9514 | #00C0AF | 0.8043 | None |
| TP53INP2 | -0.2140 | -0.4946 | #B79F00 | 0.8041 | None |
| DROSHA | -0.4111 | -0.6031 | #00BA38 | 0.8040 | None |
| ASAP1 | -0.0896 | -0.6031 | #00BA38 | 0.8032 | None |
| DLGAP4 | -0.3307 | -0.6031 | #00BA38 | 0.8022 | 5 |
| ETV6 | -0.1418 | -0.6031 | #00BA38 | 0.8011 | None |
| CACNG3 | -0.4689 | -0.6031 | #00BA38 | 0.8008 | None |
| GATAD2B | -0.4221 | -0.6031 | #00BA38 | 0.8008 | None |
| ATN1 | -0.2052 | -0.6031 | #00BA38 | 0.7982 | None |
| RASGRF1 | -0.7425 | -0.9514 | #00C0AF | 0.7981 | None |
| DAAM1 | 0.1579 | -0.0094 | #00A7FF | 0.7978 | None |
| NRXN3 | -0.6716 | -0.9514 | #00C0AF | 0.7977 | 3 |
| RIMBP2 | 0.2615 | -0.0094 | #00A7FF | 0.7969 | None |
| HUWE1 | -0.5026 | -0.6031 | #00BA38 | 0.7968 | None |
| NFIX | -0.4208 | -0.6031 | #00BA38 | 0.7966 | None |
| TLN2 | -0.4783 | -0.9514 | #00C0AF | 0.7962 | None |
| CELF2 | -0.0605 | -0.9514 | #00C0AF | 0.7951 | None |
| GNAS | -0.5865 | -0.6031 | #00BA38 | 0.7949 | 4 |
| POM121C | -0.2791 | -0.6031 | #00BA38 | 0.7945 | None |
| SETD1B | -0.1561 | -0.6031 | #00BA38 | 0.7939 | 4 |
| ZNF804A | -0.2768 | -0.6750 | #D376FF | 0.7935 | 3 |
| SAP130 | -0.2482 | -0.6031 | #00BA38 | 0.7922 | None |
| ARID1A | -0.1378 | -0.6031 | #00BA38 | 0.7920 | None |
| HIVEP2 | 0.0165 | -0.9514 | #00C0AF | 0.7919 | None |
| NBEA | -0.4147 | -0.9514 | #00C0AF | 0.7915 | 4 |
| CLIP3 | -0.5368 | -0.6031 | #00BA38 | 0.7906 | None |
Negative samples distribution
Selecting the Negative samples in the test set
negative_set = test_set %>% filter(!SFARI)
negative_set_table = negative_set %>% apply_labels(prob = 'Assigned Probability',
pred = 'Label Prediction')cro(negative_set_table$pred)|  #Total | |
|---|---|
|  Label Prediction | |
| Â Â Â FALSEÂ | 9730 |
| Â Â Â TRUEÂ | 5407 |
|    #Total cases | 15137 |
cat(paste0('\n', sum(negative_set$pred), ' genes are predicted as ASD-related'))##
## 5407 genes are predicted as ASD-relatednegative_set %>% ggplot(aes(prob)) + geom_density(color='#F8766D', fill='#F8766D', alpha=0.5) +
geom_vline(xintercept=0.5, color='#333333', linetype='dotted') +
ggtitle('Probability distribution of the Negative samples in the test set') +
theme_minimal()
Probability and Gene Significance
There’s a lot of noise, but the probability the model assigns to each gene seems to have a negative relation with the Gene Significance (under-expressed genes having on average the higher probabilities and over-expressed genes the lowest)
The pattern is strongest in under-expressed genes
negative_set %>% ggplot(aes(prob, GS, color=MTcor)) + geom_point() + geom_smooth(method='loess', color='#666666') +
geom_hline(yintercept=0, color='gray', linetype='dashed') + xlab('Probability') +
scale_color_gradientn(colours=c('#F8766D','white','#00BFC4')) +
ggtitle('Relation between Probability and Gene Significance') + theme_minimal()
Probability and Module-Diagnosis correlation
On average, the model seems to be assigning a probability inversely proportional to the Module-Diagnosis correlation of the module, with the highest positively correlated modules having the lowest average probability and the highest negatively correlated modules the highest average probability. But the difference isn’t big
negative_set %>% ggplot(aes(MTcor, prob, color=GS)) + geom_point() + geom_smooth(method='loess', color='#666666') +
geom_hline(yintercept=mean(negative_set$prob), color='gray', linetype='dashed') +
scale_color_gradientn(colours=c('#F8766D','#F8766D','white','#00BFC4','#00BFC4')) +
xlab('Modules ordered by their correlation to ASD') + ylab('Model probability') +
theme_minimal()
Summarised version, plotting by module instead of by gene
The difference in the trend lines between this plot and the one above is that the one above takes all the points into consideration while this considers each module as an observation by itself, so the top one is strongly affected by big modules and the bottom one treats all modules the same
The model seems to give higher probabilities to genes belonging to modules with a small (absolute) correlation to Diagnosis (this is unexpected)
plot_data = negative_set %>% group_by(MTcor) %>% summarise(mean = mean(prob), sd = sd(prob), n = n()) %>%
mutate(MTcor_sign = ifelse(MTcor>0, 'Positive', 'Negative')) %>% left_join(original_dataset, by='MTcor') %>%
dplyr::select(Module, MTcor, MTcor_sign, mean, sd, n) %>% distinct()
colnames(plot_data)[1] = 'ID'
ggplotly(plot_data %>% ggplot(aes(MTcor, mean, size=n, color=MTcor_sign)) + geom_point(aes(id=ID)) +
geom_smooth(method='loess', color='gray', se=FALSE) + geom_smooth(method='lm', se=FALSE) +
xlab('Module-Diagnosis correlation') + ylab('Mean Probability by Model') + theme_minimal())Probability and level of expression
There is a positive relation between level of expression and probability, the model seems to be capturing indirectly the level of expression of the genes to make the prediction, so it’s introducing the same bias
# Gandal dataset
load('./../Data/preprocessed_data.RData')
datExpr = datExpr %>% data.frame
DE_info = DE_info %>% data.framemean_and_sd = data.frame(ID=rownames(datExpr), meanExpr=rowMeans(datExpr), sdExpr=apply(datExpr,1,sd))
plot_data = negative_set %>% left_join(mean_and_sd, by='ID') %>%
left_join(original_dataset %>% mutate(ID=rownames(original_dataset)) %>%
dplyr::select(ID, Module), by='ID')
colnames(plot_data)[ncol(plot_data)] = 'Module'
plot_data %>% ggplot(aes(meanExpr, prob)) + geom_point(alpha=0.2, color='#0099cc') +
geom_smooth(method='loess', color='gray', alpha=0.3) +
geom_smooth(method='lm', color='#999999', se=FALSE, alpha=1) +
theme_minimal() + ggtitle('Mean expression vs model probability by gene')
rm(mean_and_sd)plot_data2 = plot_data %>% group_by(Module) %>% summarise(meanExpr = mean(meanExpr), meanProb = mean(prob), n=n())
ggplotly(plot_data2 %>% ggplot(aes(meanExpr, meanProb, size=n)) + geom_point(color=plot_data2$Module) +
geom_smooth(method='loess', se=TRUE, color='gray', alpha=0.1, size=0.7) +
geom_smooth(method='lm', se=FALSE, color='gray') + theme_minimal() + theme(legend.position='none') +
ggtitle('Mean expression vs model probability by Module'))rm(plot_data2)Probability and lfc
There is a relation between probability and lfc, so it **IS*() capturing a bit of true information (because lfc and mean expression were negatively correlated and it still has a positive relation in the model)
- The relation is stronger in genes under-expressed in ASD
plot_data = negative_set %>% left_join(DE_info %>% mutate(ID=rownames(DE_info)), by='ID')
plot_data %>% ggplot(aes(log2FoldChange, prob)) + geom_point(alpha=0.1, color='#0099cc') +
geom_smooth(method='loess', color='gray', alpha=0.3) +
theme_minimal() + ggtitle('lfc vs model probability by gene')
- The relation is stronger in Differentially Expressed genes
p1 = plot_data %>% filter(log2FoldChange<0) %>% mutate(DE = padj<0.05) %>% ggplot(aes(log2FoldChange, prob, color=DE)) + geom_point(alpha=0.1) +
geom_smooth(method='loess', alpha=0.1) + xlab('') + ylab('Probability') +
ylim(c(min(plot_data$prob), max(plot_data$prob))) +
theme_minimal() + theme(legend.position = 'none', plot.margin=unit(c(1,-0.3,1,1), 'cm'))
p2 = plot_data %>% filter(log2FoldChange>=0) %>% mutate(DE = padj<0.05) %>% ggplot(aes(log2FoldChange, prob, color=DE)) + geom_point(alpha=0.1) +
geom_smooth(method='loess', alpha=0.1) + xlab('') + ylab('Probability') + ylab('') +
scale_y_continuous(position = 'right', limits = c(min(plot_data$prob), max(plot_data$prob))) +
theme_minimal() + theme(plot.margin = unit(c(1,1,1,-0.3), 'cm'), axis.ticks.y = element_blank())
grid.arrange(p1, p2, nrow=1, top = 'LFC vs model probability by gene', bottom = 'LFC')
rm(p1, p2)Conclusion
The model is capturing the mean level of expression of the genes (indirectly through module memberhsip), which is a strong bias found in the SFARI scores, but it seems to be capturing a bit of true biological signal as well (based on the GS and the log fold change plots)
Saving results
predictions = test_set
save(predictions, dataset, file='./../Data/Ridge_model_robust.RData')Session info
sessionInfo()## R version 3.6.3 (2020-02-29)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 18.04.4 LTS
##
## Matrix products: default
## BLAS: /usr/lib/x86_64-linux-gnu/blas/libblas.so.3.7.1
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.7.1
##
## locale:
## [1] LC_CTYPE=en_GB.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_GB.UTF-8 LC_COLLATE=en_GB.UTF-8
## [5] LC_MONETARY=en_GB.UTF-8 LC_MESSAGES=en_GB.UTF-8
## [7] LC_PAPER=en_GB.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_GB.UTF-8 LC_IDENTIFICATION=C
##
## attached base packages:
## [1] stats graphics grDevices utils datasets methods base
##
## other attached packages:
## [1] expss_0.10.2 corrplot_0.84 car_3.0-7 carData_3.0-3
## [5] ROCR_1.0-7 gplots_3.0.3 caret_6.0-86 lattice_0.20-41
## [9] Rtsne_0.15 biomaRt_2.40.5 RColorBrewer_1.1-2 gridExtra_2.3
## [13] viridis_0.5.1 viridisLite_0.3.0 plotly_4.9.2 knitr_1.28
## [17] forcats_0.5.0 stringr_1.4.0 dplyr_0.8.5 purrr_0.3.3
## [21] readr_1.3.1 tidyr_1.0.2 tibble_3.0.0 ggplot2_3.3.0
## [25] tidyverse_1.3.0
##
## loaded via a namespace (and not attached):
## [1] readxl_1.3.1 backports_1.1.5
## [3] Hmisc_4.4-0 plyr_1.8.6
## [5] lazyeval_0.2.2 splines_3.6.3
## [7] BiocParallel_1.18.1 crosstalk_1.1.0.1
## [9] GenomeInfoDb_1.20.0 digest_0.6.25
## [11] foreach_1.5.0 htmltools_0.4.0
## [13] gdata_2.18.0 fansi_0.4.1
## [15] magrittr_1.5 checkmate_2.0.0
## [17] memoise_1.1.0 cluster_2.1.0
## [19] openxlsx_4.1.4 annotate_1.62.0
## [21] recipes_0.1.10 modelr_0.1.6
## [23] gower_0.2.1 matrixStats_0.56.0
## [25] prettyunits_1.1.1 jpeg_0.1-8.1
## [27] colorspace_1.4-1 blob_1.2.1
## [29] rvest_0.3.5 haven_2.2.0
## [31] xfun_0.12 crayon_1.3.4
## [33] RCurl_1.98-1.1 jsonlite_1.6.1
## [35] genefilter_1.66.0 survival_3.1-11
## [37] iterators_1.0.12 glue_1.3.2
## [39] gtable_0.3.0 zlibbioc_1.30.0
## [41] ipred_0.9-9 XVector_0.24.0
## [43] DelayedArray_0.10.0 shape_1.4.4
## [45] BiocGenerics_0.30.0 abind_1.4-5
## [47] scales_1.1.0 DBI_1.1.0
## [49] Rcpp_1.0.4 xtable_1.8-4
## [51] progress_1.2.2 htmlTable_1.13.3
## [53] foreign_0.8-75 bit_1.1-15.2
## [55] Formula_1.2-3 stats4_3.6.3
## [57] lava_1.6.7 prodlim_2019.11.13
## [59] glmnet_3.0-2 htmlwidgets_1.5.1
## [61] httr_1.4.1 acepack_1.4.1
## [63] ellipsis_0.3.0 pkgconfig_2.0.3
## [65] XML_3.99-0.3 farver_2.0.3
## [67] nnet_7.3-13 dbplyr_1.4.2
## [69] locfit_1.5-9.4 tidyselect_1.0.0
## [71] labeling_0.3 rlang_0.4.5
## [73] reshape2_1.4.3 AnnotationDbi_1.46.1
## [75] munsell_0.5.0 cellranger_1.1.0
## [77] tools_3.6.3 cli_2.0.2
## [79] generics_0.0.2 RSQLite_2.2.0
## [81] broom_0.5.5 evaluate_0.14
## [83] yaml_2.2.1 ModelMetrics_1.2.2.2
## [85] bit64_0.9-7 fs_1.4.0
## [87] zip_2.0.4 caTools_1.18.0
## [89] nlme_3.1-147 xml2_1.2.5
## [91] compiler_3.6.3 rstudioapi_0.11
## [93] png_0.1-7 curl_4.3
## [95] e1071_1.7-3 reprex_0.3.0
## [97] geneplotter_1.62.0 stringi_1.4.6
## [99] highr_0.8 Matrix_1.2-18
## [101] vctrs_0.2.4 pillar_1.4.3
## [103] lifecycle_0.2.0 data.table_1.12.8
## [105] bitops_1.0-6 GenomicRanges_1.36.1
## [107] latticeExtra_0.6-29 R6_2.4.1
## [109] KernSmooth_2.23-16 rio_0.5.16
## [111] IRanges_2.18.3 codetools_0.2-16
## [113] MASS_7.3-51.5 gtools_3.8.2
## [115] assertthat_0.2.1 SummarizedExperiment_1.14.1
## [117] DESeq2_1.24.0 withr_2.1.2
## [119] S4Vectors_0.22.1 GenomeInfoDbData_1.2.1
## [121] mgcv_1.8-31 parallel_3.6.3
## [123] hms_0.5.3 grid_3.6.3
## [125] rpart_4.1-15 timeDate_3043.102
## [127] class_7.3-16 rmarkdown_2.1
## [129] pROC_1.16.2 base64enc_0.1-3
## [131] Biobase_2.44.0 lubridate_1.7.4